MCQ
A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1cm and the height of the cone is equal to its radius. The volume of the solid is
- ✓$\pi \ cm ^3$
- B$4 \pi \ cm^3$
- C$2 \pi \ cm^3$
- D$3 \pi \ cm^3$
✓
Answer
Correct option: A.
$\pi \ cm ^3$
Radii of cone $=r=1 \ cm$
Radius of hemisphere $= r =1 \ cm( h )=1 \ cm$
Height of cone $(h)=1 h=1 \ cm$
Volume of solid $=$ Volume of cone $+$ Volume of a hemisphere
$=\frac{1}{3} \pi r^2 h+\frac{2}{3} \pi r^3=\frac{1}{3} \pi r^2(h+2 r)$
$=\frac{1}{3} \times \pi \times(1)^2(1+2 \times 1)$
$=\frac{1}{3} \times \pi \times 3$
$=\pi \ cm ^3$
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